Skeptical and Optimistic Robust Priors for Clinical Trials

Abstract

A useful technique from the subjective Bayesian viewpoint, suggested by Spiegelhalter et al. (1994), is to ask the subject matter researchers and other parties involved, such as pharmaceutical companies and regulatory bodies, for reasonable optimistic and pessimistic priors regarding the effectiveness of a new treatment. Up to now, the proposed skeptical and optimistic priors have been limited to conjugate priors, though there is no need for this limitation. The same reasonably adversarial points of view can be taken with robust priors. A recent reference with robust priors usefully applied to clinical trials is in Fuquene, Cook, and Pericchi (2009). Our proposal in this paper is to use Cauchy and intrinsic robust priors for both skeptical and optimistic priors leading to results more closely related with the sampling data when prior and data are in conflict. In other words, the use of robust priors removes the dogmatism implicit in conjugate priors.